Efficient estimation and verification of quantum many-body systems
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Date
2019-10-17
Authors
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Publication Type
Dissertation
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Abstract
Quantum systems and tensors share the property that the complexity of their description grows exponentially with the number of physical subsystems or tensor indices. This thesis discusses efficient methods for tensor reconstruction, quantum state estimation and verification, as well as quantum state and process tomography. The methods proposed here can be efficient in the sense that the resource requirements scale only polynomially instead of exponentially with the number of physical subsystems or tensor indices. In numerical and analytical calculations, matrix product state (MPS)/tensor train (TT), projected entangled pair state (PEPS), and hierarchical Tucker representations are used. The reconstruction and estimation methods are discussed in principle, their performance is evaluated with numerical simulations, and the quantum state in an ion trap quantum simulator experiment is estimated and verified.
Description
Faculties
Fakultät für Naturwissenschaften
Institutions
Institut für Theoretische Physik
Institut für Komplexe Quantensysteme
Institut für Komplexe Quantensysteme
Citation
DFG Project uulm
JUSTUS / HPC-Cluster Theoretische Chemie / DFG / 236232410
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Standard (ohne Print-on-Demand)
Keywords
Quantum state estimation, Quantum state tomography, Quantum process tomography, Ancilla-assisted process tomography, Quantum time evolution, Matrix product state, Matrix product operator, Tensor train, Projected entangled pair state, Tucker representation, Tensor reconstruction, Lieb-Robinson bound, Maximum likelihood estimation, Singular value thresholding, Quantenzustand, Spannungstensor, Maximum-Likelihood-Schätzung, Schwellenwert, Tensor fields, Quantum theory-Mathematics, Mathematical physics, DDC 500 / Natural sciences & mathematics, DDC 530 / Physics